Battlefield-level group movement trend arrow drawing method

Abstract

The application discloses a battle-level group movement situation arrow drawing method, comprising the following steps: S1, establishing a group target movement track, establishing a group target movement track representing the whole group according to the movement track of each group target; S2, arrow type judgment; S3, determining arrow master control points and slave control points; S4, rendering the control points and drawing arrows. The application solves the problem that in the prior art, control points are manually selected, time and effort are consumed, and real-time battle situation cannot be timely reflected, and in addition, solves the problem that in the prior art, control points generated directly by original tracks can be overlapped, leading to serious deformation of arrows.

Description

Technical Field

[0001] This invention belongs to the field of data visualization technology, and in particular relates to a data-driven method for drawing arrows representing campaign-level group movement patterns. Background Technology

[0002] Military maps are maps that use symbols and text to depict military situations. They can clearly display complex military situations on a map and are widely used in military command, training, and academic research. Military symbols on military maps can be divided into regular symbols and random symbols. Arrows, which belong to the category of random symbols, are mainly used to reflect information such as the evolution of the battlefield situation, the enemy's offensive posture, the intentions and trends of multiple offensives, and are the most commonly used graphic symbols in various military activities such as military command, sand table simulations, adversarial exercises, and multi-army drills.

[0003] However, like other random military symbols, arrows have variable directions and shapes, making them a key challenge in military mapping system research. Currently, scholars have proposed several methods for drawing arrows; however, existing methods typically require manual drawing of fixed control points rather than data-driven drawing. Therefore, the drawn arrows are displayed statically on maps and cannot be adjusted to reflect real-time battlefield conditions.

[0004] Furthermore, in the evolution of the battlefield situation at the campaign level, commanders mostly focus on the movement of group targets at the cluster level. Group movement situation arrows enable commanders to clearly, efficiently, quickly, and accurately grasp the core forces of all parties on the battlefield and their main offensive postures. However, there are often many moving targets in a large cluster, which will generate many trajectory data that change over time. However, existing arrow drawing methods rarely involve the representation of the overall situation. Currently, most group situation arrow drawing methods use manual selection of control points, which is time-consuming and laborious, and cannot reflect the real-time situation of the campaign in a timely manner. In addition, the control points generated by the existing technology directly using the original trajectory may overlap, resulting in serious arrow deformation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for drawing arrows representing the movement of a group, so as to reflect the movement of a group at the campaign level in real time through data-driven methods.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is a method for drawing arrows representing the movement of a large group at the campaign level, comprising:

[0007] S1: Establish the movement trajectory of the group targets. Based on the movement trajectory of each group target, establish a group target movement trajectory that represents the entire group.

[0008] S2: Arrow type determination, specifically including:

[0009] S21: Calculate the center curve L corresponding to the fitted group target movement trajectory;

[0010] S22: Calculate the distance H between the first and last points of the central curve L, H = |D FitEnd -D FitStart |;

[0011] Among them, D FitEnd D is the endpoint of the center curve L. FitStart Let R be the first endpoint of the central curve L. D is the straight line MN obtained by connecting the first and last points of the curve L, and the distance D from the midpoint R of the curve L to the straight line MN is calculated.

[0012] S23: Determine the arrow type. The specific determination method is as follows:

[0013] If D / H < d r If , then it is a straight arrow;

[0014] If D / H≥d r Then it is a curved arrow; where d r A threshold set by the user;

[0015] S3: Determine the primary and secondary control points of the arrow, specifically including:

[0016] The master control point is a point on the center curve that is bound to the original data;

[0017] Select several control points from the arrow based on the points on the center curve L and the tangent to the center curve L;

[0018] S4: Render control points and draw arrows.

[0019] Furthermore, S1 specifically includes:

[0020] S11: Calculate the movement trajectory of group targets, based on the campaign-level group targets over a period of time [T] start T end Movement trajectory data within ]{[D 1start D 1start+1 D 1start+2 ...D 1start+i ..., D 1end ], [D 2start D 2start+1 D 2start+2 ...D 2start+i ..., D 2end ], [D 3start D 3start+1 D 3start+2 ...D3start+i ..., D 3end ],...,[D Nstart D Nstart+1 D Nstart+2 ...D Nstart+i ..., D Nend ]}, calculate the average value of the target trajectory data:

[0021]

[0022] A trajectory representing the movement of the group is obtained [D] MeanStart D MeanStart+1 D MeanStart+2 ...D MeanStart+i ...D MeanEnd ], where T start At the start time, T end D is the end time. 1start+i Let D be the coordinates of the first group target at the i-th time, N be the total number of group targets, and i be the coordinates of the i-th time from the initial time. MeanStart+i Let start be the coordinate of the average value of N target trajectory data at time i, representing the movement trajectory of the group. start represents the starting time and end represents the last time.

[0023] S12: Fit the movement of the group target. Use a cubic Bézier curve to interpolate and fit the trajectory of the group target movement obtained in S11 to optimize the trajectory. Determine the arrow type to obtain the fitted trajectory of the group target movement [D]. FitStart D FitStart+1 D FitStart+2 ...D FitStart+i ...D FitEnd ], D FitStart+i It is the coordinate of the curve fitted to the movement trajectory of a group at the i-th time.

[0024] Preferably, the threshold d in S1 r Set it to 0.1.

[0025] Furthermore, S21 specifically includes:

[0026] The original cubic Bézier curve B(t) is: B(t) = (1-t) 3 ×P0+3t(1-t) 2 ×P1+3t 2 (1-t)×P2+t 3 ×P3

[0027] Where P0 is the starting point of the curve, P2 is the first control point, P3 is the second control point, and t is a parameter with a value range of [0,1]. Then the center curve L(t) is:

[0028] L(t)=(1-t) 3 ×D MeanStart+i +3t(1-t) 2 ×D MeanStart+i+1 +3t 2 (1-t)×D MeanStart+i+2 +t 3 ×D MeanStart+i+3 .

[0029] Furthermore, S3 also includes: calculating the distance S of the center curve L, the method for calculating the distance S of the center curve L is as follows:

[0030] S=Σ(|(D FitStart+1 -D FitStart )|+|(D FitStart+2 -D FitStart+1 )|+…+|(D FitEnd -D FitEnd-1 )|).

[0031] Furthermore, the main control points are control point P0 at the head of the arrow and control point P9 at the tail of the arrow. The main control point P0 is the first endpoint of the center curve L, i.e., data point D. FitEnd The main control point P9 is the tail endpoint of the center curve L, i.e., data point D. FitStart .

[0032] Furthermore, methods for determining control points include:

[0033] Determine two secondary control points on each side of the arrowhead. A secondary control point is a point not located on the center line; specifically, it includes:

[0034] (1) Draw the tangent line L to the center curve L through the main control point P0 at the head of the arrow. P1 ;

[0035] (2) Draw a line from P0 to the tangent line L. P1 Two straight lines L with an angle of θ1 01 With L 02 In L 01 With L 02 Select two control points P1 and P2 on either side of the arrowhead, ensuring the distance d from P1 to control point P0 is... 10 The distance d from control point P2 to control point P0 20 They are equal and satisfy equation d. 10 =d 20 =d1, where d1 is a constant;

[0036] Determine two control points inside the arrowhead, and draw a line through P0 intersecting the tangent line L. P1 Two straight lines L with an angle of ... 03 With L 04 , among which, in L 03 With L 04 Select two control points P3 and P4 inside the arrowhead, ensuring the distance d from P3 to P0 is... 30 The distance d from P4 to P0 40 They are equal and satisfy equation d. 30 =d 40 =d2, where d2 is a constant and d2 < d1;

[0037] Determine the two control points for the arrow's tail fin, specifically including:

[0038] (1) Draw the tangent line L to the center curve L through the main control point P9 at the tail of the arrow. P2 p;

[0039] (2) Draw a line from P9 to the tangent line L. P2 Two straight lines L with an angle of ... 05 With L 06 In L 05 With L 06 Select two control points, P5 and P6, on the upper arrow tail wing, ensuring the distance d from P5 to P9. 59 The distance d from control points P6 to P9 69 They are equal and satisfy equation d. 59 =d 69 =d3, where d3 is a constant;

[0040] Identify two control points in the middle of the arrow shaft, specifically including:

[0041] (1) On the central curve L, take a point P that is 0.6S away from the main control point P0 at the head of the arrow. Draw the tangent line L to the central curve L through point P. P3 ;

[0042] (2) Draw a tangent line L through point P. P3 perpendicular line L 12 and on line L 12 Choose two control points P7 and P8 in the middle of the arrow shaft, located on opposite sides of point P. When the arrow type is a straight arrow, equation d is satisfied. 7P =d 8P =d4, and when the arrow type is a curved arrow, the equation d is satisfied. 7P =4d 8P =4d4 or d 8P =4d 7P = 4d⁴, where d⁴ is a constant, d 7PLet d be the distance from point P7 to point P. 8P Let be the distance from point P8 to point P.

[0043] Furthermore, the method for rendering control points and drawing arrows is specifically as follows:

[0044] Based on the generated control points, the arrow body is smoothly connected using Bézier curves to draw the complete arrow and render it.

[0045] The d3 interpolator is used to achieve a smooth transition between different arrows.

[0046] Furthermore, the specific settings for θ1 and d1 are as follows: when the arrow type is a straight arrow, θ1 = 45° and d1 = 0.36S; when the arrow type is a curved arrow, θ1 = 60° and d1 = 0.5S.

[0047] The specific settings for θ2 and d2 are as follows: when the arrow type is a straight arrow, θ2 = 26.5° and d2 = 0.285S; when the arrow type is a curved arrow, θ2 = 50° and d2 = 0.3S.

[0048] The specific settings for θ3 and d3 are as follows: when the arrow type is a straight arrow, θ3 = 66.8° and d3 = 0.375S; when the arrow type is a curved arrow, θ3 = 20° and d3 = 0.625S.

[0049] The setting of d4 is that d4 = 0 when the arrow type is a straight arrow. 197 S; When the arrow type is a curved arrow, d4 = 0. 25 S.

[0050] The beneficial effects of this invention are:

[0051] 1. It realizes fully data-driven arrow drawing. The drawn situation arrows can automatically adjust with changes in war data. Compared with manual arrow drawing, it is more efficient and can automatically adjust with changes in war data to reflect the real-time situation.

[0052] 2. A trajectory representing the movement of a group of targets is calculated using the average value method. Control points are set based on the center curve of this trajectory and a specific angle. Finally, an arrow representing the movement trajectory of the group is drawn, which more clearly and accurately represents the movement of group targets on the battlefield at the campaign level on the map.

[0053] 3. By fitting the trajectory through Bezier interpolation and then determining the arrow type, a smooth transition can be achieved between different types of arrows, which more vividly represents the movement of the group. Moreover, it solves the problem that the control points generated by directly using the original trajectory in the existing technology may overlap, resulting in severe arrow deformation. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 Draw a flowchart for the arrows representing the movement of groups at the campaign level;

[0056] Figure 2 A schematic diagram of the trajectory of a campaign-level group objective;

[0057] Figure 3 A diagram illustrating arrow type determination;

[0058] Figure 4 This is a schematic diagram of the master and slave control points for the arrow.

[0059] Figure 5 A schematic diagram of the two main control points at the head and tail of the arrow;

[0060] Figure 6 A schematic diagram showing the two control points on either side of the arrowhead;

[0061] Figure 7 This is a schematic diagram of the two control points inside the arrowhead.

[0062] Figure 8 A schematic diagram of the two control points of the arrow tail fin;

[0063] Figure 9 A schematic diagram of two control points in the middle of a straight arrowhead;

[0064] Figure 10 A schematic diagram showing two control points in the middle of a curved arrowhead;

[0065] Figure 11 The final drawing of the straight arrow;

[0066] Figure 12 The final drawing of the curved arrow;

[0067] Figure 13 This is a comparison diagram of the effects of the present invention and the prior art;

[0068] Figure 14 This is an example diagram showing the direct generation of control points from the original trajectory.

[0069] Figure 15This is a diagram showing the transition effect between different time slices of the same arrow. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] See Figure 1 The steps of the technical solution of the present invention are as follows:

[0072] S1: Establish the movement trajectory of the group target, specifically including:

[0073] S11: Calculate the movement trajectory of the group of targets. Figure 2 For the movement trajectory of each group of targets, based on the campaign-level group targets over a period of time [T] start T end Movement trajectory data within ]{[D 1start D 1start+1 D 1start+2 ...D 1start+i ..., D 1end ], [D 2start D 2start+1 D 2start+2 ...D 2start+i ..., D 2end ], [D 3start D 3start+1 D 3start+2 ...D 3start+i ..., D 3end ],...,[D Nstart D Nstart+1 D Nstart+2 ...D Nstart+i ..., ..., D Nend ]}, calculate the average value of the target trajectory data:

[0074]

[0075] A trajectory representing the movement of the group is obtained [D] MeanStart D MeanStart+1 D MeanStart+2 ...D MeanStart+i ...D MeanEnd ], where T start At the start time, T end D is the end time. 1start+iLet D be the coordinates of the first group target at the i-th moment, N be the total number of group targets, and i be the time interval (i.e., time slice) between two adjacent moments from the initial moment. This time slice is manually set based on the specific type of war and experience. For air warfare (duration 10-20 minutes), the preferred time slice is 1 second. For land or sea warfare (duration 5 hours-3 days), a time slice of 1 minute is preferred. MeanStart+i Let start be the coordinates of a movement trajectory representing a group (i.e., the average of N target trajectory data) at the i-th time point, where start represents the starting time and end represents the last time point.

[0076] S12: Fit the movement of the group target. Use a cubic Bézier curve to interpolate and fit the movement trajectory of the group target obtained in S11 to optimize the trajectory and facilitate arrow type determination, thus obtaining the fitted movement trajectory of the group target [D]. FitStart D FitStart+1 D FitStart+2 ...D FitStart+i ...D FitEnd ]. D FitStart+i It is the coordinate of the curve at the i-th time point after fitting a curve representing the movement trajectory of a group (i.e., the average value of N target trajectory data).

[0077] S2: Arrow type determination, specifically including:

[0078] S21: Calculate the center curve L corresponding to the fitted group target movement trajectory, specifically including:

[0079] The original cubic Bézier curve B(t) is: B(t) = (1-t) 3 ×P0+3t(1-t) 2 ×P1+3t 2 (1-t)×P2+t 3 ×P3 Where P0 is the starting point of the curve, P2 is the first control point, P3 is the second control point, and t is a parameter with a value range of [0,1].

[0080] Then L(t) on the central curve is:

[0081] L(t)=(1-t) 3 ×D MeanStart+i +3t(1-t) 2 ×D MeanStart+i+1 +3t 2 (1-t)×D MeanStart+i+2 +t 3 ×D MeanStart+i+3 .

[0082] S22: Calculate the distance H between the first and last points of the central curve L, H = |DFitEnd -D FitStart |;

[0083] Given the first and last points of curve L, obtain the straight line MN, and calculate the distance D from the midpoint R of curve L to the straight line MN; S23: See Figure 3 To determine the arrow type, the specific method is as follows:

[0084] If D / H < d r Then it is a straight arrow.

[0085] If D / H≥d r , then it is a curved arrow;

[0086] According to human visual perception, when d r When the threshold is ≥0.1, human vision can clearly distinguish between straight and curved arrows. Therefore, this invention sets the threshold d... r Set to 0.1;

[0087] S3: See also Figure 4 Determine the primary and secondary control points of the arrow, specifically including:

[0088] S31: Calculate the distance S of the center curve L. The method for calculating the distance S of the center curve L is as follows:

[0089] S

[0090] =Σ(|(D FitStart+1 -D FitStart )|+|(D FitStart+2 -D FitStart+1 )|+…+|(D FitEnd -D FitEnd-1 )|)

[0091] S32: Determine the control points:

[0092] Determine the two main control points at the head and tail of the arrow, see... Figure 5 The master control point is a point on the center curve that is bound to the original data. Based on the data-driven principle, the algorithm first determines two master control points: control point P0 at the head of the arrow and control point P9 at the tail of the arrow. Master control point P0 is the starting endpoint of the center curve L, i.e., data point D. FitEnd The main control point P9 is the tail endpoint of the center curve L, i.e., data point D. FitStart ;

[0093] Determine the two control points on either side of the arrowhead, see... Figure 6 Control points refer to points that are not located on the center line, as detailed below:

[0094] (1) Draw the tangent line L to the center curve L through the main control point P0 at the head of the arrow. P1;

[0095] (2) Draw a line from P0 to the tangent line L. P1 Two straight lines L with an angle of θ1 01 With L 02 In L 01 With L 02 Select two control points P1 and P2 on either side of the arrowhead, ensuring the distance d from P1 to control point P0 is... 10 The distance d from control point P2 to control point P0 20 They are equal and satisfy equation d. 10 =d 20 =d1, where d1 is a constant. In this step, both θ1 and d1 are adjustable parameters. Considering the overall aesthetics of the arrow and the visual perception effect of humans, when the arrow type is a straight arrow, this invention recommends empirical parameters θ1 = 60° and d1 = 0.5S. When the arrow type is a curved arrow, this invention recommends empirical parameters θ1 = 60° and d1 = 0.5S.

[0096] Determine the two control points inside the arrowhead, see... Figure 7 , pass through P0 and the tangent line L P1 Two straight lines L with an angle of () 03 With L 04 In L 03 With L 04 Select two control points P3 and P4 inside the arrowhead, ensuring the distance d from P3 to P0 is... 30 The distance d from P4 to P0 40 They are equal and satisfy equation d. 30 =d 40 =d2, where d2 is a constant (d2 < d1). In this step, both θ2 and d2 are adjustable parameters. Considering the overall aesthetics of the arrow and the visual perception effect of humans, when the arrow type is a straight arrow, this invention recommends empirical parameters. When the arrow type is a curved arrow, this invention recommends empirical parameters θ2 = 50° and d2 = 0. 3 S;

[0097] Determine the two control points for the arrow's tail fin, see... Figure 8 The details are as follows:

[0098] (1) Draw the tangent line L to the center curve L through the main control point P9 at the tail of the arrow. P2 p;

[0099] (2) Draw a line from P9 to the tangent line L. P2 Two straight lines L with an angle of θ3 05 With L 06 In L 05 With L 06Select two control points, P5 and P6, on the upper arrow tail wing, ensuring the distance d from P5 to P9. 59 The distance d from control points P6 to P9 69 They are equal and satisfy equation d. 59 =d 69 =d3, where d3 is a constant. In this step, both θ3 and d3 are adjustable parameters. Considering the overall aesthetics of the arrow and the visual perception effect of humans, when the arrow type is a straight arrow, the present invention recommends empirical parameters. When the arrow type is a curved arrow, the present invention recommends empirical parameters θ3 = 20° and d3 = 0.625S.

[0100] Determine the two control points in the middle of the arrow shaft, see Figure 9 and Figure 10 The details are as follows:

[0101] (1) On the central curve L, take a point P that is 0.6S away from the main control point P0 at the head of the arrow. Draw the tangent line L to the central curve L through point P. P3 ;

[0102] (2) Draw a tangent line L through point P. P3 perpendicular line L 12 and on line L 12 The invention selects two control points, P7 and P8, located on opposite sides of point P in the middle of the arrow shaft. When the arrowhead type is a straight arrow, the invention ensures that the distance d from P7 to P is... 7P The distance d from P8 to P 8P They are equal and satisfy equation d. 7P =d 8P =d4, and when the arrow type is a curved arrow, the present invention ensures that equation d is satisfied. 7P =4d 8P =4d4 or d 8P =4d 7P =4d4, this invention determines d based on the direction of the arrow's curvature. 7P With d 8P The size of the arrow, where d4 is a constant. In this step, d4 is an adjustable parameter. Considering the overall aesthetics of the arrow and the visual perception effect of humans, this invention recommends an empirical parameter when the arrow type is a straight arrow and when the arrow type is a curved arrow, this invention recommends an empirical parameter d4 = 0.25S.

[0103] S4: Render control points and draw the arrow. Based on the generated 10 control points P0-P9, use Bézier curves to smoothly connect the arrow body to draw the complete arrow. See [link / reference] Figure 11 and Figure 12 And render the arrows;

[0104] The d3 interpolator is used to achieve a smooth transition between different arrows.

[0105] This invention enables fully data-driven arrow drawing. The drawn situational arrows can automatically adjust to changes in war data, making it more efficient than manually drawn arrows and reflecting real-time situational changes. By calculating a trajectory representing the movement of a group of targets using the averaging method, and setting control points based on the center curve of this trajectory and specific angles, arrows representing the movement trajectory of the group are finally drawn, more clearly and accurately representing the movement of group targets on the battlefield at the campaign level on the map. After fitting the trajectory using Bezier interpolation, the arrow type is determined, and different types of arrows more vividly represent the movement of the group.

[0106] Figure 13 The left side shows the arrow drawing effect of the prior art, and the right side shows the arrow drawing effect of the present invention. The present invention uses Bezier interpolation to fit the trajectory, which solves the problem that the control points generated by directly using the original trajectory in the prior art may have issues. Figure 14 The problem of overlapping arrows causing severe deformation.

[0107] The situational arrows drawn by this invention can automatically adjust to changes in war data, reflecting real-time situational awareness. Smooth transitions can be achieved between different types of arrows. Figure 15 .

[0108] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0109] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for drawing arrows representing the movement of a group at the campaign level, characterized in that, include: S1: Establish the movement trajectory of the group targets. Based on the movement trajectory of each group target, establish a group target movement trajectory that represents the entire group. S2: Arrow type determination, specifically including: S21: Calculate the center curve L corresponding to the fitted group target movement trajectory; S22: Calculate the distance H between the first and last points of the central curve L. ; Among them, D FitEnd D is the endpoint of the center curve L. FitStart Let R be the first endpoint of the central curve L. D is the straight line MN obtained by connecting the first and last points of the curve L, and the distance D from the midpoint R of the curve L to the straight line MN is calculated. S23: Determine the arrow type. The specific determination method is as follows: if D / H < d r If , then it is a straight arrow; if D / H ≥ d r Then it is a curved arrow; where d r A threshold set by the user; S3: Determine the primary and secondary control points of the arrow, specifically including: The master control point is a point on the center curve that is bound to the original data; Select several control points from the arrow based on the points on the center curve L and the tangent to the center curve L; S4: Render control points and draw arrows; S1 specifically includes: S11: Calculate the movement trajectory of group targets, based on the campaign-level group targets over a period of time [T] start T end Movement trajectory data within ]{[D 1start D 1start+1 D 1start+2 ,... D 1start+i ..., D 1end ], [D 2start D 2start+1 D 2start+2 ,... D 2start+i ..., D 2end ], [D 3start D 3start+1 D 3start+2 ,... D 3start+i ..., D 3end ],...,[D Nstart D Nstart+1 D Nstart+2 ,... D Nstart+i ..., D Nend ]}, calculate the average value of the target trajectory data: ； Obtain a target movement trajectory representing the entire group [D] MeanStart D MeanStart+1 , D MeanStart+2 ...D MeanStart+i ...D MeanEnd ], where T start At the start time, T end D is the end time. 1start+i Let D be the coordinates of the first target in the entire group at the i-th time, N be the total number of targets in the entire group, and i be the coordinates of the i-th time from the initial time. MeanStart+i Let start be the coordinate of the average value of N target trajectory data at time i, representing the movement trajectory of the entire group. start represents the starting time and end represents the last time. S12: Fit the movement of the group target. Use a cubic Bézier curve to interpolate and fit the trajectory of the group target movement obtained in S11 to optimize the trajectory. Determine the arrow type to obtain the fitted trajectory of the entire group target movement. [D] FitStart D FitStart+1 D FitStart+2 ...D FitStart+i ...D FitEnd ], D FitStart+i It is the coordinate of the curve fitted to the movement trajectory of the entire group at the i-th time. S21 specifically includes: The original cubic Bézier curve B(t) is: ; in, H 0 is the starting point of the curve. H 1. First control point H 2 is the second control point, and t is a parameter with a value range of [0,1]. Then the central curve L(t) is: 。 2. The method for drawing arrows representing the movement of a group at the campaign level according to claim 1, characterized in that, The threshold in S23 d r Set it to 0.

1.

3. The method for drawing arrows representing the movement of a group at the campaign level according to claim 1, characterized in that, S3 further includes: calculating the length S of the center curve L, wherein the method for calculating the length S of the center curve L is as follows: 。 4. The method for drawing arrows representing the movement of a group at the campaign level according to claim 3, characterized in that, The main control points are control point P0 at the head of the arrow and control point P9 at the tail of the arrow. The main control point P0 is the first endpoint of the center curve L, i.e., data point D. FitEnd The main control point P9 is the tail endpoint of the center curve L, i.e., data point D. FitStart .

5. The method for drawing arrows representing the movement of a group at the campaign level according to claim 4, characterized in that, The method for determining the control point includes: Determine two secondary control points on each side of the arrowhead. A secondary control point is a point not located on the center line; specifically, it includes: (1) Draw the tangent line L to the center curve L through the main control point P0 at the head of the arrow. P1 ; (2) Draw a line from P0 to the tangent line L. P1 The angle measure is The two straight lines L 01 With L 02 In L 01 With L 02 Select two control points P1 and P2 on either side of the arrowhead, ensuring the distance d from P1 to control point P0 is... 10 The distance d from control point P2 to control point P0 20 They are equal and satisfy equation d. 10 =d 20 =d1, where d1 is a constant; Determine two control points inside the arrowhead, and draw a line through P0 intersecting the tangent line L. P1 The angle measure is The two straight lines L 03 With L 04 ,in In L 03 With L 04 Select two control points P3 and P4 inside the arrowhead, ensuring the distance d from P3 to P0 is... 30 The distance d from P4 to P0 40 They are equal and satisfy equation d. 30 =d 40 =d2, where d2 is a constant and d2 < d1; Determine the two control points for the arrow's tail fin, specifically including: (1) Draw the tangent line L to the center curve L through the main control point P9 at the tail of the arrow. P2 ; (2) Draw a line from P9 to the tangent line L. P2 The angle measure is The two straight lines L 05 With L 06 In L 05 With L 06 Select two control points, P5 and P6, on the upper arrow tail wing, ensuring the distance d from P5 to P9. 59 The distance d from control points P6 to P9 69 They are equal and satisfy equation d. 59 =d 69 =d3, where d3 is a constant; Identify two control points in the middle of the arrow shaft, specifically including: (1) Take a point P on the center curve L, which is 0.6S away from the main control point P0 at the head of the arrow. Draw the tangent line L to the center curve L through point P. P3 ; (2) Draw a tangent line L through point P. P3 perpendicular line L 12 and on line L 12 Choose two control points P7 and P8 in the middle of the arrow shaft, located on opposite sides of point P. When the arrow type is a straight arrow, equation d is satisfied. 7P =d 8P =d4, and when the arrow type is a curved arrow, the equation d is satisfied. 7P =4d 8P =4d4 or d 8P =4d 7P =4d⁴, where d⁴ is a constant, d 7P Let d be the distance from point P7 to point P. 8P Let be the distance from point P8 to point P.

6. The method for drawing arrows representing the movement of a group at the campaign level according to claim 1, characterized in that, The method for rendering control points and drawing arrows is as follows: Based on the generated control points, the arrow body is smoothly connected using Bézier curves to draw the complete arrow and render it. The D3 interpolator is used to achieve a smooth transition between different arrows.

7. The method for drawing arrows representing the movement of a group at the campaign level according to claim 5, characterized in that, The The specific settings for d1 are as follows: when the arrow type is a straight arrow, When the arrow type is a curved arrow, ; The The specific settings for d2 are as follows: when the arrow type is a straight arrow, When the arrow type is a curved arrow, ; The The specific settings for d3 are as follows: when the arrow type is a straight arrow, When the arrow type is a curved arrow, ; The setting of d4 is as follows: when the arrow type is a straight arrow... When the arrow type is a curved arrow, .

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